Time orientations and complex structure. Following [1]}, [2]}, we have expressed the difference between \(\mathcal {J}(\mathcal {A})\)  and \(\mathcal {A}\)  in terms of time orientations in Def. REF . As exponentials of dynamical correspondences [3]}, time orientations highlight the double role played by self-adjoint operators: as observables and generators of dynamics in quantum mechanics [4]}, [5]}. This perspective has some appeal when considering axiomatic reconstructions of quantum mechanics and possible generalisations they suggest.
